Plasma expansion and current flow in a vacuum arc with a small anode

A low-density plasma flow in a vacuum arc with a small anode, which intercepts only part of the cathodic plasma jet, was studied theoretically using a two-dimensional approximation. The plasma expansion was modeled using the sourceless steady-state hydrodynamic equations, where the free boundary of the plasma was determined by a self-consistent solution of the gasdynamic and electrical current equations. Magnetic forces from the azimuthal self-magnetic field were taken into account. The influence of the ratio of the anode radius to initial plasma jet radius on the plasma density, velocity, current distribution, and anode sheath potential drop is analyzed. It is shown that the mass and current flow in a 500 A arc are compressed near the axis. This leads to an increase in the plasma density by a factor of two and in the axial current density by a factor of 1.5.